1

SPCSPC

SPC is a method to operate process efficiently using statistical methods.

To identify sources of variation.

Applicable when mistake proofing cannot be done .

SPC uses control charts to monitor the process.

SPC is a monitoring Instrument.

2

VARIATIONVARIATION

Random Natural for the process

Predictable

Occurs randomly over time

Also called common cause variation

Generally process remains in control

Non- RandomNot a part of natural process.

Unexpected , Sporadic variation

result of some specific assignable cause

Also called special called variation

Process go out of control

Control charts display the total variation in the process so it can be monitored and kept in control (within its operating capability)

3

Nxi

22 )( µ

σ−

= ∑Population variance (σ2)

nXi

X ∑=

Sample mean (X-bar)

Nxi∑=µ

Population mean (µ)

Population Std Deviation(σ)

)( 2σσ =

Estimate for Std Deviation(s)

)( 2ss =

1)( 2

2

−−

= ∑n

xxs i

Estimate for variance (s2)

Sample StatisticsSample StatisticsPopulation StatisticsPopulation Statistics

Population and Sample StatisticsPopulation and Sample Statistics

4

Introduction to Control ChartsIntroduction to Control Charts

PFD

5

TYPES OF CONTROL CHARTSTYPES OF CONTROL CHARTSDATA TYPE

Continuous Defect Defective

Subgroup size Subgroup size Subgroup size

N=1 IMR Chart

N=2~9 XR Chart

N=>9 XS Chart

Fixed C Chart

Variable U Chart

Fixed NP Chart

Variable P Chart

Quantitative

Variable’s

Qualitative

Attribute

6

CONTROL CHARTSCONTROL CHARTS

Control charts are designed to prevent defect occurrence in advance & control process variation efficiently by detecting and addressing the occurrence of assignable cause in the process

Control chart consists of

Center line CL= Sample mean (m)

Upper Control limit = m+3σ ( Control limits are at a distance of 3σ from mean)

Lower control limit = m-3σ

Control chart deals with analysis of process , process control &Control chart deals with analysis of process , process control & to to judge if the product under study is acceptable or notjudge if the product under study is acceptable or not

7

DESIGNING CONTROL CHART

Suppose we have a process that we assume the true process mean is µ = 74 and the process standard deviation is σ = 0.01. Samples of size 5 are taken giving a standard deviation of the sample average, is

0045.0501.0

nx ==σ

=σ

8

• Control limits can be set at 3 standard deviations from the mean in both directions.

• “3-Sigma Control Limits” UCL = 74 + 3(0.0045) = 74.0135

CL= 74LCL = 74 - 3(0.0045) = 73.9865

DESIGNING CONTROL CHART

9

Introduction to Control Charts

Rational Subgroups

Constructing Rational Subgroups• Select consecutive units of production.

– Provides a “snapshot” of the process.– Good at detecting process shifts.

• Select a random sample over the entire sampling interval.– Good at detecting if a mean has shifted – out-of-control and then back in-control.

10

WHAT DO WE CHECK IN THE CHARTSWHAT DO WE CHECK IN THE CHARTS

The Automotive Industry Action Group (AIAG) suggests using the following

guidelines to test for special causes:

■ Test 1: 1 point > 3 standard deviations from center line1 point > 3 standard deviations from center line

■ Test 2: 9 points in a row on the same side of center line9 points in a row on the same side of center line

■ Test 3: 6 points in a row, all increasing or all decreasing6 points in a row, all increasing or all decreasing

Also additional to these tests we can also check

Test 4: 14 points in a row ,alternating up & down14 points in a row ,alternating up & down

Test 5: 2 out of 3 points > 2 standard deviation from center line (same 2 out of 3 points > 2 standard deviation from center line (same side). Too much Variationsside). Too much Variations

Test 6: 4 out of 5 points > 1 standard deviation from center line (same 4 out of 5 points > 1 standard deviation from center line (same side).Too much Variationsside).Too much Variations

Test 7 : 15 points in a row within 1 standard deviation of center line (e15 points in a row within 1 standard deviation of center line (either side).Measurement error ither side).Measurement error

Test 8 : 8 points in a row > 1 standard deviations from center line (eith8 points in a row > 1 standard deviations from center line (either side). Mixture of dataer side). Mixture of data

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IMR CHART (SUB GROUP SIZE=1)IMR CHART (SUB GROUP SIZE=1)

Torque is measured daily once , in first half hour and recordedTorque is measured daily once , in first half hour and recorded . . Draw a suitable control chart to find if it is in control or notDraw a suitable control chart to find if it is in control or not

I-MR Chart

1) IMR charts is used when data is slow , that is time range &1) IMR charts is used when data is slow , that is time range & Collection is pretty large.Collection is pretty large.

2) There is one value per subgroup.2) There is one value per subgroup.

3) There is one between variation and no within variation.3) There is one between variation and no within variation.

4) Range between adjacent data points (moving range) is used to4) Range between adjacent data points (moving range) is used to control process standard control process standard deviation.deviation.

EXAMPLEEXAMPLE

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ANALYSIS OF IMR CHARTANALYSIS OF IMR CHART

Date

Ind

ivid

ua

l V

alu

e

07/30/200507/27/200507/24/200507/21/200507/18/200507/15/200507/12/200507/09/200507/06/200507/03/2005

7.2

6.9

6.6

6.3

6.0

_X=6.431

UC L=7.072

LC L=5.790

Date

Mo

vin

g R

an

ge

07/30/200507/27/200507/24/200507/21/200507/18/200507/15/200507/12/200507/09/200507/06/200507/03/2005

0.8

0.6

0.4

0.2

0.0

__MR=0.2410

UC L=0.7875

LC L=0

I-MR Chart of Torque

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XX-- R CONTROL CHART (1<Sub group Size<5)R CONTROL CHART (1<Sub group Size<5)

X chart is used to control process mean X chart is used to control process mean

R chart uses the differences between the maximum & minimum of thR chart uses the differences between the maximum & minimum of the observed e observed values in sample , to control process variationvalues in sample , to control process variation

XX--R chart is useful to control both mean and variation at the sameR chart is useful to control both mean and variation at the same timetime

Example

Data collected for 5 m/c for a part reading over 20 hrs find the behavior of the process for the

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Sample

Sa

mp

le M

ea

n

2018161412108642

9.00

8.85

8.70

8.55

8.40

__X=8.636

UC L=8.9644

LC L=8.3076

Sample

Sa

mp

le R

an

ge

2018161412108642

1.2

0.9

0.6

0.3

0.0

_R=0.569

UC L=1.204

LC L=0

MC process variation

ANALYSIS OF X Bar R CHARTANALYSIS OF X Bar R CHART

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XX-- R CONTROL CHART CONSTANTSR CONTROL CHART CONSTANTS

SAMPLE SIZE A2 D3 D4 d2

2

3

4

5

6

7

8

9

10

1.880 0 3.267

1.023 0 2.574

00.729

0.577

2.282

1.023

2.004

1.924

0.483

0.149 0.076

0.373 1.864

0

0

0.1840.337

0.136

1.816

0.308 0.223 1.777

UCL (R)= R D4

LCL (R)= R D3

UCL(X)= X A2 R

LCL(X)= X A2 R

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RESULT X bar R RESULT X bar R

R Chart R Chart ––

Asses the process variation is in control.Asses the process variation is in control.

Consists of plotted points for subgroup ranges .Consists of plotted points for subgroup ranges .

Four tests are conducted for special causes to detect points Four tests are conducted for special causes to detect points beyond the control limits and specific patterns in data.beyond the control limits and specific patterns in data.

A failed point(marked in RED) indicates that there is non randomA failed point(marked in RED) indicates that there is non randompattern (special cause variation).pattern (special cause variation).

In the given data:In the given data:--

None of the subgroup ranges are outside the control limitsNone of the subgroup ranges are outside the control limits

The points inside the limits display a random pattern.The points inside the limits display a random pattern.

There is no lack of control in variation .There is no lack of control in variation .

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RESULT X bar RRESULT X bar R

X Chart X Chart

A failed point indicates that there is a NonA failed point indicates that there is a Non--random pattern random pattern due to special cause variation.due to special cause variation.

The R chart must be in control before X bar is interpreted.The R chart must be in control before X bar is interpreted.

Results are shown in the session window.Results are shown in the session window.

If the process is stable, how capable is it can be determined If the process is stable, how capable is it can be determined by capability calculation.by capability calculation.

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COMPARISON BETWEEN COMPARISON BETWEEN X bar X bar RR & X bar & X bar SS

BOTH S CHARTS & R CHARTS

-- Measure Subgroup variability. Measure Subgroup variability.

--Give the estimate of the process standard deviation & Control liGive the estimate of the process standard deviation & Control limits.mits.

Represent SpreadRepresent Spread

SS RR

CalculatesCalculates

AccuracyAccuracy

Sensitivity to VariationSensitivity to Variation

ApplicationApplication

Using Standard Deviation

Using Range

Uses complete data Uses Max & Min Values

Better

Greater

For higher subgroup size( >5 ),high rate of production ,data collection is quick & in expensive or when increased sensitivity is desired.

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CONTROL CHART FOR DEFECTIVESCONTROL CHART FOR DEFECTIVES

P Chart’sP Chart’s

P Charts are used for defectives when SUB GROUP size is VariablP Charts are used for defectives when SUB GROUP size is Variable.e.

Data follows binomial distribution. Data follows binomial distribution. P(n, N) = pP(n, N) = pnn.(1 .(1 -- p)p)NN--nn..NNCCnn

Can be used for supplier lot quality on the basis of delivery.Can be used for supplier lot quality on the basis of delivery.

The P chart consists of the following:The P chart consists of the following:

Plotted points, which represent the proportion of defectives. Plotted points, which represent the proportion of defectives.

Center line (green), which is the average proportion defectiveCenter line (green), which is the average proportion defective

Control limits (red), which are located 3 s above and below the Control limits (red), which are located 3 s above and below the center line and provide a visual center line and provide a visual means for when the process is out of control. The control limitsmeans for when the process is out of control. The control limits are either fixed or varied, are either fixed or varied, depending on your data and choices:depending on your data and choices:

When your sample sizes are the same or when you choose to use anWhen your sample sizes are the same or when you choose to use an average sample size, then average sample size, then the control limits will be fixed. In this case, tests for speciathe control limits will be fixed. In this case, tests for special causes may be conducted.l causes may be conducted.

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Sample

Prop

orti

on

10987654321

0.018

0.016

0.014

0.012

0.010

0.008

0.006

0.004

0.002

_P=0.00968

UCL=0.01627

LCL=0.00310

P Chart of Number of Defectives

Tests performed with unequal sample sizes

Sample size is differentSample size is different

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P Chart result analysisP Chart result analysis

When your sample sizes vary, then the control limits will vary. When your sample sizes vary, then the control limits will vary. In this case, tests for special causes cannot be conducted. You In this case, tests for special causes cannot be conducted. You should examine the P chart for points outside the control limitsshould examine the P chart for points outside the control limitsand trends or other nonrandom patterns.and trends or other nonrandom patterns.

Four tests are conducted for special causes by Minitab.Four tests are conducted for special causes by Minitab.

Plotted points representing the PROPRTION OF DEFECTIVES.Plotted points representing the PROPRTION OF DEFECTIVES.

Center line (green) , which is the average proportion Center line (green) , which is the average proportion defective.defective.

Control limit (red) either fixed or varied , depending on data.Control limit (red) either fixed or varied , depending on data.

P Chart for the given data shows process in control.P Chart for the given data shows process in control.

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NP CHART FOR DEFECTIVES (SUB GROUP SIZE SAME)NP CHART FOR DEFECTIVES (SUB GROUP SIZE SAME)

Use NP charts to examine the number of defectives in each sampleUse NP charts to examine the number of defectives in each sample and and determine whether or not the process is in control. The NP chartdetermine whether or not the process is in control. The NP chart consists of consists of the following:the following:

Plotted points, which represent the number of defectives for eaPlotted points, which represent the number of defectives for each samplech sample

Center line (green), which is the average number of defectivesCenter line (green), which is the average number of defectives

Control limits (red), which are located 3 s above and below theControl limits (red), which are located 3 s above and below the center line center line and provide a visual means for assessing when to take action on and provide a visual means for assessing when to take action on the the process. process.

For every lot of 100 Bush manufactured ,13 are randomly inspecteFor every lot of 100 Bush manufactured ,13 are randomly inspected & reported for defectives .Find the data is d & reported for defectives .Find the data is in control.in control.

Example:

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GRAPHGRAPH

Sample

Sam

ple

Coun

t

30272421181512963

9

8

7

6

5

4

3

2

1

0

__NP=3.1

UCL=7.709

LCL=0

1

NP Chart for 13 randomly slected subgroup size

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TEST 1. One point more than 3.00 standard TEST 1. One point more than 3.00 standard deviations from center line.deviations from center line.

Test Failed at points: 23Test Failed at points: 23

Test Results for NP Chart of No. of defectivesTest Results for NP Chart of No. of defectives

NP chart should not be used for variable sample size because theNP chart should not be used for variable sample size because thecontrol limits & center line changes when sample size changes macontrol limits & center line changes when sample size changes making king NP chart difficult to interpret.NP chart difficult to interpret.

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CONTROL CHART FOR DEFECT ( C CHART)CONTROL CHART FOR DEFECT ( C CHART)

SUB GROUP SIZE IS FIXEDSUB GROUP SIZE IS FIXED

Used to find defects as DPU (defects / unit) of the controlled Used to find defects as DPU (defects / unit) of the controlled process.process.

Inspection unit must be fixed.Inspection unit must be fixed.

Inspection units can more than one if the data is not Inspection units can more than one if the data is not classified by the type of defect.classified by the type of defect.

Example:Example:

Following is the defect quantity per lot of bush manufactured , check the data is in control or not

26

Lot_no.

Sam

ple

Coun

t

5045403530252015105

9

8

7

6

5

4

3

2

1

0

_C=2.48

UCL=7.204

LCL=0

1

C Chart of No. of defects

GRAPHGRAPH

1 point outside the control limit

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C Chart of No. of defects C Chart of No. of defects

Test Results for C Chart of No. of defects

TEST 1. One point more than 3.00 standard deviations from centerTEST 1. One point more than 3.00 standard deviations from center line.line.

Test Failed at points: 13Test Failed at points: 13

* WARNING * If graph is updated with new data, the results a* WARNING * If graph is updated with new data, the results above may no bove may no longer be correct.longer be correct.

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CONTROL CHART FOR DEFECT ( U CHART)CONTROL CHART FOR DEFECT ( U CHART)

SUB GROUP SIZE IS VARIABLESUB GROUP SIZE IS VARIABLE

Used to asses the Used to asses the number of defects per unit of measurement to number of defects per unit of measurement to determine if the process is in control.determine if the process is in control.

If the samples are of same size or when the average sample size If the samples are of same size or when the average sample size is taken , is taken , Control limits will beControl limits will be FIXED.FIXED.

when the sample size vary , when the sample size vary , Control limits vary,Tests for special causes Control limits vary,Tests for special causes cannot be conducted.cannot be conducted.

EXAMPLEEXAMPLE

Find the given data is in control or not , sample size is not fiFind the given data is in control or not , sample size is not fixed. xed.

29

Week_No.

Sam

ple

Coun

t Pe

r Un

it

2018161412108642

4

3

2

1

0

_U=1.5

UCL=3.337

LCL=0

1

U Chart of No. of Defects

Tests performed with unequal sample sizes

GRAPHGRAPH

30

Results for: U_defectsResults for: U_defects

TESTTEST 1.1. One point more than 3.00 standard One point more than 3.00 standard deviations from center line.deviations from center line.

Test Failed at points: 1Test Failed at points: 1

* WARNING * If graph is updated with new * WARNING * If graph is updated with new data, the results above may nodata, the results above may no

* longer be correct.* longer be correct.

31

RUN CHART (Test for randomness of Data)RUN CHART (Test for randomness of Data)

Run charts are plotted to find special patterns in data :Run charts are plotted to find special patterns in data :1)1) MixturesMixtures

2)2) ClustersClusters

3)3) TrendsTrends

4)4) OscillationsOscillations

Create a Run chart from the same data in which U charts are prepCreate a Run chart from the same data in which U charts are preparedared

32

Sample

No. o

f D

efec

ts

18161412108642

14

12

10

8

6

4

2

0

Number of runs about median:

0.54621

9Expected number of runs: 9.21053Longest run about median: 5Approx P-Value for Clustering: 0.45379Approx P-Value for Mixtures:

Number of runs up or down:

0.57562

12Expected number of runs: 12.33333Longest run up or down: 2Approx P-Value for Trends: 0.42438Approx P-Value for Oscillation:

Run Chart of No. of Defects

GRAPH ANALYSISGRAPH ANALYSIS

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A normal pattern for a process in control is one of randomness. If only common causes of variation exist in your process, the data will exhibit random behavior.

Run Chart provides two tests for randomness:

·Based on the number of runs about the median.

·Based on the number of runs up or down.

Test for Randomness Condition Indication

Number of runs about theNumber of runs about the More runs observed thanMore runs observed than Mixed data from twoMixed data from two

medianmedian expected populationsexpected populations

Fewer runs obsFewer runs observed than Clustering of dataerved than Clustering of data

expectedexpected

Number of runs up or down More runs observed than Oscillation - data varies

Fewer runs observed thanFewer runs observed than Trending of dataTrending of data

expectedexpected

Oscillation: It suggests that process is not in a controlled staOscillation: It suggests that process is not in a controlled state(depends upon P value).te(depends upon P value).

Trends: Trends may warn that a process is about to go out oTrends: Trends may warn that a process is about to go out of control, and may f control, and may be due to such factors as worn tool, Change in operator etc.be due to such factors as worn tool, Change in operator etc.